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This question is not about a particular situation in the game, but rather how to study the game in the sense of if I wanted to learn Scrabble, I would spend time focusing on how certain uncommon letters can be used in words of length X or the goals of different strategies.

If no one had ever played Risk before, how would we go about learning to evaluate which moves are better for a particular situation?

4 Answers
4

This is purely off the top of my head, but the following come to mind:

Learn the most likely die rolls

Look at paths of contact (eg, you can only get to Australia through Siam)

Find "choke points" (building off the contact paths)

Note that Continent bonuses are in proportion to not only size, but difficulty in holding/winning them

Gameplay can be wildly different with two players instead of 3, 4, 5, or 6

ultimately all games devolve into 2 player games, but knowing how to handle the higher number of players is key to surviving long enough to be in the final pairing

The Neutral player in a 2 player game can have some interesting consequences when playing strictly

because they are not required to be eliminated to win, you might only attack to gain a Risk card

depending on how the cards were dealt, they can be used to your (or the other player's) advantage as a buffer to weaken attacks (or strengthen defense), forcing the attacker to expend more armies to defeat the defender

Everything else I can think of come with time and practice:

like when to attack / when not to attack

for example, if your contact territories are heavily defended, but your non-contact territories only have one or two armies, it may be a Bad Idea™ to attack from there if the enemy territories are moderately-well defended (ie, they could attack back form multiple directions easily against a weakened contact territory and wipe-out the middle of your holdings)

when to hold cards / when to turn them in

for example, if you know that your opponent must turn his cards in on his next turn (he has 5, and therefore has a set), but you have the option (perhaps you have a set, but you have four cards, and can therefore wait a turn), it may be worthwhile holding yours till after he turns his in to get the next-higher army value from them

in my experience, holding your trades only notably impacts the game early on (before the turn-in exceeds 10 armies)

etc

And don't forget the psychology of the game, too:

Some players "want" Africa and will do [almost] anything to get/keep it (for example)

Can you expand on the middle section, about how to actually learn from time and practice? Like for instance if I could record the moves in every game, how would I then use that information to get better? How would I develop a strategy for when to hold/turn in cards from time and practice?
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Nick LarsenOct 27 '10 at 16:35

The thing that seperates the newbies from the intermediate players in RISK is:

KNOW WHEN TOSTOPATTACKING.

Essentially, the inexperienced player will look at the board, look at the forces he has, the forces the enemy has, realize that he has enough men to carry the day, and attack. He is, however, looking at the wrong pieces.

Instead, a player should look at the forces he has, the forces the enemy has, and then consider how many of his men would survive his planned attack, comparing those pieces to how many men the enemy will have available to retaliate with on his next turn. Its not enough to take territory (except for throwaway attacks for the sake of a Risk Card). One must take the territory with sufficient survivors to hold it next turn.

It is helpful to know your odds of winning any given battle over a territory. Doing that involves quite a bit more than just learning the most likely die rolls. This paper from Mathematics Magazine: www4.stat.ncsu.edu/~jaosborn/research/osborne.mathmag.pdf gives some nice charts and tables and an overall pretty readable analysis of win/lose odds, and expected losses.

This is a nice site with more information on Risk strategies than I thought was possible :) I remember spending several hours procrastinating reading over this site. They also sell a book which looks good, though I can't say I've read it.